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CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2 · Question 3(a)

Section B (Module 2). The sequence \{u_n\} is given by u_1 = 1 and u_{n+1} = (n + 1)u_n, n \ge 1.

Prove by Mathematical Induction that u_n = n! for all n \in \mathbb{N}.

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Other parts of this question

  1. 3(b)(i)Find the n-th term of S.[5 marks]
  2. 3(b)(ii)Show that S is a geometric progression.[2 marks]
  3. 3(b)(iii)Find the first term and common ratio of S.[2 marks]
  4. 3(b)(iv)Deduce the sum to infinity of S.[2 marks]

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